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Medical Statistics
Practice 1
Tao Yuchun
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Review
I. Basic concepts
1. Population and Sample
•Randomization
2. Probability and Frequency
3. Parameter and Statistic
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II. Types of data
1. Numerical Variable (Measurement Data)
•quantitatively
2. Categorical Variable (Enumeration Data)
•qualitatively
•Nominal Variable
•Count Data
3. Ordinal variable ( Rank data )
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III. The Basic Steps of Statistical Work
1. Design of study
2. Collection of data
3. Data Sorting
4. Data Analysis
• Descriptive statistics
• Inferential statistics
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IV. Statistical Description for Measurement
Data
1.1 Frequency Distribution
(1) Steps of establishing a frequency table
(2) Frequency plot ---histogram
(3) The use of frequency table
• central tendency
• measure of dispersion
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1.2 Measures for Average ★
(1) Arithmetic Mean (mean)
μ
X
n
X 1  X 2  ...  X n
X
n
X X


i 1
n
i
n
•Suitable to symmetric distribution.
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(2) Geometric Mean (G)
G  n X1 X 2  X n
lg X
lg X 1  lg X 2  ...  lg X n
1 
G  lg (
)  lg (
)
n
n
•lg-1 =10x
1
•Suitable to positive skew distribution,
like geometric progression.
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(3) Median (M)
a. For raw data
•Ranking the data, finding the middle value.
For odd number, it is; for even number, it is
mean of two middle values.
b. For frequency table
i n
M  L
(  f L )
fM 2
•Suitable to all kinds of data, but usually to
positive skew distribution.
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Add: Percentile --- Px
i
Px  L  (n  x%  f L )
fx
•Symmetric
•Positive skew
1.3 Measures for variability ★
(1) Range (R)
R = Maximum - Minimum
•Suitable to all kinds of data, but no useful.
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(2) InterQuartile Range (IQR)
IQR  Q3  Q1  P75  P25
•Suitable to all kinds of data, but usually skew
distribution.
(3) Variance and Standard Deviation (S2 and S)
2

(
X

X
)
S2 
n 1
( X  X ) 2
X 2  (X ) 2 / n
S

n 1
n 1
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•Suitable to symmetric distribution.
(4) Coefficient of Variation (CV)
S
CV   100%
X
• Comparison of the variation of two variables
with different dimensions or bigger difference
of means .
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Calculative tools
I. Scientific calculator
• The scientific calculator with statistical
function. (like CASIO fx-3600PV or CASIO fx-82TL)
• Calculative method is often:
Input all raw data, press the special
button under statistical mode, you will
get the result (like X , S) directly.
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II. Excel ★
•
•
•
•
Many statistical function.
The macro of statistical analysis tool.
Using any expression directly.
Many statistical graphs.
•See the example
(stat1(English).xls)
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III. Statistical software
• Professional statistical analysis tool.
• The special data management and
statistical analysis procedure.
• The special executive commands.
• Include almost all statistical methods.
• SAS, SPSS, Stata, BDMP, …
• If you want use it, you should have to
learn another lesson.
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Practice in class
Exercise 1: the blood-glucose(mmol/L) values from
12 randomly selected patients.
5.31, 6.12, 6.53, 6.53, 6.65, 6.66, 6.71, 6.93, 7.05,
7.15, 7.21, 7.35
Please calculate the arithmetic mean, geometric
mean and median; range, quartile range and standard
deviation.
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Exercise 2: the frequency table of latent period (day)
from 110 certain infectious disease patients.
tab2 the frequency table of latent period (day) from some infectious disease patients
latent
period
(1)
2~
4~
6~
8~
10~
12~14
total
frequency(f )
(2)
Cumulative
Frequency(∑f )
(3)
Cumulative
Frequency(%)
(4)=(3)/n
26
48
25
6
3
2
26
74
99
105
108
110
23.64
67.27
90.00
95.45
98.18
100.00
110
－
－
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1) Please calculate the arithmetic mean, geometric mean and
median, which one better reflects the average level ?
2) Please calculate the range, quartile range and standard
deviation, which one better reflects the variation ?
Answer
•See the Excel file
(practice1key.xls)
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Homework
There are raw data of temperature（℃）for 102 female
students from certain college(see below).
37.05
37.20
37.30
37.35
37.50
37.25
36.55
36.85
36.90
37.05
36.70
36.90
37.00
37.40
37.25
37.00
37.20
36.80
36.70
36.85
37.00
36.80
37.20
37.00
37.25
36.95
37.35
36.95
37.05
37.15
36.70
37.35
37.10
36.90
37.10
37.05
37.05
37.00
36.60
37.10
36.95
37.10
37.00
36.85
37.10
36.80
37.10
37.10
37.05
37.05
37.15
37.20
36.85
37.15
36.85
37.15
37.00
37.00
37.20
36.95
36.90
36.65
18
36.85
37.10
36.80
37.05
37.05
36.90
36.70
37.25
37.05
36.65
37.40
36.80
37.05
37.15
37.35
37.05
37.20
36.90
36.90
36.90
37.05
37.40
37.00
37.15
37.10
37.00
36.90
37.05
37.35
36.95
36.85
37.40
36.90
37.25
37.10
36.90
37.30
36.75
37.05
36.90
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1) Please work out a frequency table and a histogram.
2) Please calculate the arithmetic mean, median, quartile
range, standard deviation and coefficient of variation.
(http://en.wikipedia.org/wiki/Great_Wall_of_China)
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C
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CASIO
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CASIO fx-82TL
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